Nonlinear independent component analysis: Existence and uniqueness results

Neural Networks

Volumn 12, Issue 3, 1999, Pages 429-439

  Hyvärinen, Aapo ^a   Pajunen, Petteri ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Blind source separation; Feature extraction; Independent component analysis; Redundancy reduction

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONFORMAL MAPPING; CONSTRAINT THEORY; ESTIMATION; FEATURE EXTRACTION; FUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING; TWO DIMENSIONAL;

BLIND SOURCE SEPARATION; INDEPENDENT COMPONENT ANALYSIS; REDUNDANCY REDUCTION;

STATISTICAL METHODS;

ALGORITHM; ARTIFICIAL NEURAL NETWORK; MAXIMUM LIKELIHOOD METHOD; PRIORITY JOURNAL; PROBABILITY; REVIEW; STATISTICAL MODEL; THEORY;

EID: 0041435860     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(98)00140-3     Document Type: Article

References (20)

1. Ahlfors, L., 1979 Complex Analysis (3rd Ed.). New York: McGraw-Hill.
2. Barlow, H.B., 1961 Possible principles underlying the transformations of sensory messages. In: W.A. Rosenblith (Ed.), Sensory Communication (PP. 217-234). Cambridge, MA: MIT Press.
3. Barlow H.B. Single units and sensation: A neuron doctrine for perceptual psychology? Perception. 1:1972;371-394.
4. Bell A., Sejnowski T. The independent components of natural scenes are edge filters. Vision Research. 37:1997;3327-3338.
5. Burel G. Blind separation of sources: A nonlinear neural algorithm. Neural Networks. 5:(6):1992;937-947.
6. Cardoso J.-F., Laheld B.H. Equivariant adaptive source separation. IEEE Trans. on Signal Processing. 44:(12):1996;3017-3030.
7. Churchill, R.V., Brown, J.W., 1990 Complex Variables and Applications (5th Ed.). New York: McGraw-Hill.
8. Comon P. Independent component analysis - a new concept? Signal Processing. 36:1994;287-314.
9. Darmois, G., 1951 Analyse des liaisons de probabilité. In: Proc. Int. Stat. Conferences 1947, Vol. IIIA, (p. 231). Washington, D.C.
10. Deco G., Brauer W. Nonlinear higher-order statistical decorrelation by volume-conserving neural networks. Neural Networks. 8:1995;525-535.
11. Deco, G., Obradovic D. 1996 An information theoretic approach to neural computing New York: Springer.
12. Driscoll T. A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans. on Mathematical Software. 22:1996;168-186.
13. Hyvärinen, A., 1998 New approximations of differential entropy for independent component analysis and projection pursuit. In: Advances in Neural Information Processing 10 (Proc. NIPS*97) (PP. 273-279). Cambridge, MA: MIT Press.
14. Jutten C., Herault J. Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecutre. Signal Processing. 24:1991;1-10.
15. Lee, T.-W., Koehler, B., Orglmeister, R., 1997 Blind source separation of nonlinear mixing models. In: Neural networks for Signal Processing VII.
16. Olshausen B.A., Field D.J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature. 381:1996;607-609.
17. Pajunen, P., Hyvärinen, A., Karhunen, J., 1996 Nonlinear blind source separation by self-organizing maps. In: Proc. Int. Conf. on Neural Information Processing (PP. 1207-1210), Hong Kong.
18. Pajunen, P., Karhunen, J., 1997 A maximum likelihood approach to nonlinear blind source separation. In: Proc.of the 1997 Int. Conf. on Artificial Neural Networks (ICANN) (PP. 541-546). Lausanne, Switzerland.
19. Taleb, A., Jutten, C., 1997 Nonlinear source separation: The post-nonlinear mixtures. In: Proc. European Symposium on Artificial Neural Networks (ESANN97) (PP. 279-284). Bruges, Belgium.
20. Yang H.H., Amari S.-I., Cichocki A. Information-theoretic approach to blind separation of sources in nonlinear mixture. Signal Processing. 64:(3):1998;291-300.